Prof. Potter oti Hydrodynamics. 205 



of his cores in regard to softness, and partly in the manner in 

 which the experiments have been made. 



The writers support this conjecture by a number of experi- 

 ments made with defective iron and unhardened steel, wherewith 

 they are able to produce divergences quite similar to those ob- 

 sen'ed by IMiiller. The latter, however, retorts that his cylinders 

 were made of the best possible iron ; and that the reason why 

 Buff and Zamminer's results differ from his is, that their greatest 

 galvanic power was applied to their thick cores, a comparatively 

 " modest " amount of force being expended on the thin ones. 

 He contends that their results are quite in conformity with his 

 foi-mulse, and so the matter rests. 



XXVIII, On Hydrodynamics. By Professor Potter, A.M.* 



M LAGRANGE, in the tenth section of his Mecanique 

 • Analytique, page 282, says, " Mais ce n'est jamais par 

 les routes les plus simples et les plus directes, que Pesprit humain 

 parvient aux verites, de quelque genre qu'elles soient, et la 

 matiere que nous traitons en fournit un exemple frappant." The 

 subject of hydi'odynamics which called foi-th this remark is no 

 doubt one to which it emphatically applies, as is strikingly evi- 

 dent from the history of the science, which he gives. I must, 

 however, now venture to disagree with him when he says, " et 

 D'Alembert est le premier qui ait reduit les vrais lois de leur 

 mouvement a des equations analytiques." He says in another 

 place, " c'est fl Euler qu'on doit les premieres formules generales 

 ])our le mouvement des fluides, fondees sur les lois de leur equi- 

 libre, et presentees avec la notation simple et lumineuse des dif- 

 ferences partielles." If the doctrine of the atomic constitution 

 of matter had been demonstrated in the days of these great men, 

 the formulfe for fluid motion might not have required revision at 

 the present day. 



The veiy definition of a fluid, that eveiy particle is capable of 

 motion on the application of the slightest force, shows us that 

 when we admit the doctrine of ultimate atoms, we must consider 

 the motion of a fluid as originating in the motions of its consti- 

 tuent atoms ; and the dynamical principles must be applied in 

 the first instance to the distinct atoms, and not to particles of 

 fluid which may consist of either many atoms or of an imaginary 

 fraction of an atom, which has been the case as far as the theories 

 hitherto received arc concerned. It is in this respect that I have 

 long seen, as stated in my paper in the last Number of this pub- 

 lication, that the equations of fluid motion must be rectified ; 

 and having found the correct differential equation for vibratory 



* Communicated bv the Author. 



